Help needed creating 3D shapes of a divided sphere

Hi,

Can anyone offer advice on how i might go about creating the 6 individual shapes that result from vertically dividing a 3D sphere into 6 equal segments as my attached image shows?

I want to create them as individual 3D shapes that i can revolve and rotate in illustrator.

I can create a simple 3D disc by adding an Extrude & Bevel effect to a circle, but in the case of a divided sphere the surface around the circumference would be curved as opposed to flat.

I also can't work out how to create the 2 end pieces, essentially a 3D hemisphere that i can also revolve and rotate. 

Any ideas?